The concept of Value ar Risk (VaR) is now considered as the standard measure of risk. The VaR of a position is a single number attempting to measure and summarize the risk of this position. As the VaR is not in general a sufficient statistics for risk, it is interesting to know what the risk is beyond the VaR. This paper addresses the following issue: what is the expected loss of a position knowing that the loss is greater than the VaR ? A simple statistical framework is developed to answer this question and an empirical study is presented with several VaR methods: the extreme value distribution, the historical distribution, the unconditional normal distribution and conditional normal processes.
LONGIN, F. (1997). Beyond the VaR. ESSEC Business School.